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Vladimir_Nesov comments on Open Thread: July 2009 - Less Wrong
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I'm pretty sure that just can't be right. (His argument, that is. I think your interpretation of it is dead on.) We are not limited to imagining the sorts of things our brain is causally determined by. And the way you just put it seems completely backwards. Even if everything reduces to quarks, it's only in principle-- our brains are hard wired to create multiple levels of models, and could never conceive of an explanation of a 747 in terms of quarks.
Look at it this way. Can a painting have a subject? Can it be "about" something? Of course. Certainly there's nothing supernatural about this, but there's also nothing legitimate on the level of quarks that could be used to differentiate between a painting that has a subject and a painting that is just random blobs. I can imagine, after all, two paintings, almost identical in their coordinate-positioning of quarks, which have completely different subjects. I can also imagine two paintings, very different in terms of coordinates of quarks (perhaps painted with two different materials) which have the same subject. So while everything reduces down to quarks, it's the easiest thing in the world to explain a painting's about-ness on a separate level from quarks, and completely impossible to envision an explanation for this about-ness in terms of quarks.
I'm just not sure what about a "black ball" misses the mark of conceivability.
This is a good example of how the "natural" concepts are actually quite elaborate, paying utmost attention to tiny details that are almost invisible in other representations. But these details are in fact there, in the territory. The fact that they are small in one representation doesn't belittle their significance in another representation. And the fact that one object is placed in one high-level category and a "slightly" different object is placed in another category results from exactly these "tiny" differences. You can't visualize these differences in terms of quarks directly, but in terms of other high-level categories it is exactly what you are doing: keeping track of the tiny distinctions that are important to you for some reason.
That sounds right, but that sounds like I am (or at least could) visualize these levels as separate, since to keep track of the tiny differences that end up being important is impossible for my mind to do. This seems to necessitate that imagining irreducibility is not only possible, but natural (and perhaps unavoidable?).
This is not to say that irreducibility is logical, and our reason may insist to us that the painting is indeed reducible to quarks, whether or not we can imagine this reduction. But collapsing the levels is not the default position, a priori logically neccessary.
I'm not entirely clear on what you are saying above. Your mind keeps many overlapping concepts that build on each other. It's also incapable of introspecting on this process in detail, or of representing one concept explicitly in terms of an arbitrary other concept, even if the model in the mind supports a lawful dependence between them. You can only visualize some concepts in the context of some other closely related concepts. Notice that we are only talking about the algorithm of human mind and its limitations.
Perhaps it would help (since I think I've lost you as well) to relate this all back to the original question: is all levels reducing down to a common lowest level a priori logically necessary? My contention is that it's possible to reduce the levels, but not logically necessary-- and I support this contention with the fact that we don't necessarily collapse the levels in our reasoning, and we can't collapse the levels in our imagination. If you weren't disagreeing with this, then I've just misunderstood you, and I apologize.
There are at least 3 ways for anti-reductionism to be not only clearly consistent, but with some plausibility, true - in the sense that there is empirical as well as conceptual evidence for every position (This is connected to a quote I posted yesterday):
Ontological monism: The whole universe is prior to its parts (see this paper)
No fundamental level: The descent of levels is infinite (see that paper)
"Causation" is an inconsistent concept (I'm one free afternoon and two karma points away from a top-level post on this ;)